Renormalization Group Theory for a Perturbed KdV Equation

We show that renormalization group(RG) theory can be used to give an analytic description of the evolution of a perturbed KdV equation. The equations describing the deformation of its shape as the effect of perturbation are RG equations. The RG approach may be simpler than inverse scattering theory(IST) and another approaches, because it dose not rely on any knowledge of IST and it is very concise and easy to understand. To the best of our knowledge, this is the first time that RG has been used in this way for the perturbed soliton dynamics.Comment: 4 pages, no figure, revte

Electron-Electron Interactions and the Hall-Insulator

Using the Kubo formula, we show explicitly that a non-interacting electron system can not behave like a Hall-insulator, {\it ie.,} a DC resistivity matrix $\rho_{xx}\rightarrow\infty$ and $\rho_{xy}=$finite in the zero temperature limit, as has been observed recently in experiment. For a strongly interacting electron system in a magnetic field, we illustrate, by constructing a specific form of correlations between mobile and localized electrons, that the Hall resistivity can approximately equal to its classical value. A Hall-insulator is realized in this model when the density of mobile electrons becomes vanishingly small. It is shown that in non-interacting electron systems, the zero-temperature frequency-dependent conductacnce generally does not give the DC conductance.Comment: 11 pages, RevTeX3.

Grain boundary pinning and glassy dynamics in stripe phases

We study numerically and analytically the coarsening of stripe phases in two spatial dimensions, and show that transient configurations do not achieve long ranged orientational order but rather evolve into glassy configurations with very slow dynamics. In the absence of thermal fluctuations, defects such as grain boundaries become pinned in an effective periodic potential that is induced by the underlying periodicity of the stripe pattern itself. Pinning arises without quenched disorder from the non-adiabatic coupling between the slowly varying envelope of the order parameter around a defect, and its fast variation over the stripe wavelength. The characteristic size of ordered domains asymptotes to a finite value $R_g \sim \lambda_0\ \epsilon^{-1/2}\exp(|a|/\sqrt{\epsilon})$, where$\epsilon\ll 1$is the dimensionless distance away from threshold,$\lambda_0$the stripe wavelength, and$a$ a constant of order unity. Random fluctuations allow defect motion to resume until a new characteristic scale is reached, function of the intensity of the fluctuations. We finally discuss the relationship between defect pinning and the coarsening laws obtained in the intermediate time regime.Comment: 17 pages, 8 figures. Corrected version with one new figur

Dynamics of heteropolymers in dilute solution: effective equation of motion and relaxation spectrum

The dynamics of a heteropolymer chain in solution is studied in the limit of long chain length. Using functional integral representation we derive an effective equation of motion, in which the heterogeneity of the chain manifests itself as a time-dependent excluded volume effect. At the mean field level, the heteropolymer chain is therefore dynamically equivalent to a homopolymer chain with both time-independent and time-dependent excluded volume effects. The perturbed relaxation spectrum is also calculated. We find that heterogeneity also renormalizes the relaxation spectrum. However, we find, to the lowest order in heterogeneity, that the relaxation spectrum does not exhibit any dynamic freezing, at the point when static (equilibrium) ``freezing'' transition occurs in heteropolymer. Namely, the breaking of fluctuation-dissipation theorem (FDT) proposed for spin glass dynamics does not have dynamic effect in heteropolymer, as far as relaxation spectrum is concerned. The implication of this result is discussed

De novo assembly of a transcriptome from the eggs and early embryos of Astropecten aranciacus

Starfish have been instrumental in many fields of biological and ecological research. Oocytes of Astropecten aranciacus, a common species native to the Mediterranean Sea and the East Atlantic, have long been used as an experimental model to study meiotic maturation, fertilization, intracellular Ca2+ signaling, and cell cycle controls. However, investigation of the underlying molecular mechanisms has often been hampered by the overall lack of DNA or protein sequences for the species. In this study, we have assembled a transcriptome for this species from the oocytes, eggs, zygotes, and early embryos, which are known to have the highest RNA sequence complexity. Annotation of the transcriptome identified over 32,000 transcripts including the ones that encode 13 distinct cyclins and as many cyclin-dependent kinases (CDK), as well as the expected components of intracellular Ca2+ signaling toolkit. Although the mRNAs of cyclin and CDK families did not undergo significant abundance changes through the stages from oocyte to early embryo, as judged by real-time PCR, the transcript encoding Mos, a negative regulator of mitotic cell cycle, was drastically reduced during the period of rapid cleavages. Molecular phylogenetic analysis using the homologous amino acid sequences of cytochrome oxidase subunit I from A. aranciacus and 30 other starfish species indicated that Paxillosida, to which A. aranciacus belongs, is not likely to be the most basal order in Asteroidea. Taken together, the first transcriptome we assembled in this species is expected to enable us to perform comparative studies and to design gene-specific molecular tools with which to tackle long-standing biological questions